Sunday, July 24, 2016

The right answer would be “all of the above.” And that’s not because I can’t tell a point from a grapefruit, it’s because physicists can’t agree what they mean by Big Bang!

For someone in quantum gravity, the Big Bang is the initial singularity that occurs in General Relativity when the current expansion of the universe is extrapolated back to the beginning of time. At the Big Bang, then, the universe had size zero and an infinite energy density. Nobody believes this to be a physically meaningful event. We interpret it as a mathematical artifact which merely signals the breakdown of General Relativity.

If you ask a particle physicist, they’ll therefore sensibly put the Big Bang at the time where the density of matter was at the Planck scale – about 80 orders of magnitude higher than the density of a neutron star. That’s where General Relativity breaks down; it doesn’t make sense to extrapolate back farther than this. At this Big Bang, space and time were subject to significant quantum fluctuations and it’s questionable that even speaking of size makes sense, since that would require a well-defined notion of distance.

Cosmologists tend to be even more conservative. The currently most widely used model for the evolution of the universe posits that briefly after the Planck epoch an exponential expansion, known as inflation, took place. At the end of inflation, so the assumption, the energy of the field which drives the exponential expansion is dumped into particles of the standard model.
Cosmologists like to put the Big Bang at the end of inflation because inflation itself hasn’t been observationally confirmed. But they can’t agree how long inflation lasted, and so the estimates for the size of the universe range between a grapefruit and a football field.

Finally, if you ask someone in science communication, they’ll throw up their hands in despair and then explain that the Big Bang isn’t an event but a theory for the evolution of the universe. Wikipedia engages in the same obfuscation – if you look up “Big Bang” you get instead an explanation for “Big Bang theory,” leaving you to wonder what it’s a theory of.

I admit it’s not a problem that bugs physicists a lot because they don’t normally
debate the meaning of words. They’ll write down whatever equations they use, and this prevents further verbal confusion. Of course the rest of the world should also work this way, by first writing down definitions before entering unnecessary arguments.

While I am waiting for mathematical enlightment to catch on, I find this state of affairs terribly annoying. I recently had an argument on twitter about whether or not the LHC “recreates the Big Bang,” as the popular press likes to claim. It doesn’t. But it’s hard to make a point if no two references agree on what the Big Bang is to begin with, not to mention that it was neither big nor did it bang. If biologists adopted physicists standards, they’d refer to infants as blastocysts, and if you complained about it they’d explain both are phases of pregnancy theory.

I find this nomenclature unfortunate because it raises the impression we understand far less about the early universe than we do. If physicists can’t agree whether the universe at the Big Bang had the size of the White House or of a point, would you give them 5 billion dollars to slam things into each other? Maybe they’ll accidentally open a portal to a parallel universe where the US Presidential candidates are Donald Duck and Brigitta MacBridge.

Historically, the term “Big Bang” was coined by Fred Hoyle, a staunch believer in steady state cosmology. He used the phrase to make fun of Lemaitre, who, in 1927, had found a solution to Einstein’s field equations according to which the universe wasn’t eternally constant in time. Lemaitre showed, for the first time, that matter caused space to expand, which implied that the universe must have had an initial moment from which it started expanding. They didn’t then worry about exactly when the Big Bang would have been – back then they worried whether cosmology was science at all.

But we’re not in the 1940s any more, and precise science deserves precise terminology. Maybe we should rename the different stages of the universe that into “Big Bang,” “Big Bing” and “Big Bong.” This idea has much potential by allowing further refinement to “Big Bång,” “Big Bîng” or “Big Böng.” I’m sure Hoyle would approve. Then he would laugh and quote Niels Bohr, “Never express yourself more clearly than you are able to think.”

Monday, July 18, 2016

A white hole is a time-reversed black hole, an anti-collapse. While a black hole contains a region from which nothing can escape, a white hole contains a region to which nothing can fall in. Since the time-reversal of a solution of General Relativity is another solution, we know that white holes exist mathematically. But are they real?

Black holes were originally believed to merely be of mathematical interest, solutions that exist but cannot come into being in the natural world. As physicists understood more about General Relativity, however, the exact opposite turned out to be the case: It is hard to avoid black holes. They generically form from matter that collapses under its own gravitational pull. Today it is widely accepted that the black hole solutions of General Relativity describe to high accuracy astrophysical objects which we observe in the real universe.

The simplest black hole solutions in General Relativity are the Schwarzschild-solutions, or their generalizations to rotating and electrically charged black holes. These solutions however are not physically realistic because they are entirely time-independent, which means such black holes must have existed forever. Schwarzschild black holes, since they are time-reversal invariant, also necessarily come together with a white hole. Realistic black holes, on the contrary, which are formed from collapsing matter, do not have to be paired with white holes.

But there are many things we don’t understand about black holes, most prominently how they handle information of the matter that falls in. Solving the black hole information loss problem requires that information finds a way out of the black hole, and this could be done for example by flipping a black hole over to a white hole. In this case the collapse would not complete, and instead the black hole would burst, releasing all that it had previously swallowed.

Is this a plausible solution to the black hole information loss problem?

It is certainly possible to join part of the black hole solution with part of the white hole solution. But doing this brings some problems.

The first problem is that at the junction the matter must get a kick that transfers it from one state into the other. This kick cannot be achieved by any known physics – we know this from the singularity theorems. There isn’t anything in the known physics can prevent a black hole from collapsing entirely once the horizon is formed. Whatever makes this kick hence needs to violate one of the energy conditions, it must be new physics.

Something like this could happen in a region with quantum gravitational effects. But this region is normally confined to deep inside the black hole. A transition to a white hole could therefore happen, but only if the black hole is very small, for example because it has evaporated for a long time.

But this isn’t the only problem.

Before we think about the stability of black holes, let us think about a simpler question. Why doesn’t dough unmix into eggs and flour and sugar neatly separated? Because that would require an entropy decrease. The unmixing can happen, but it’s exceedingly unlikely, hence we never see it.

A black hole too has entropy. It has indeed enormous entropy. It saturates the possible entropy that can be contained within a closed surface. If matter collapses to a black hole, that’s a very likely process to happen. Consequently, if you time-reverse this collapse, you get an exceedingly unlikely process. This solution exists, but it’s not going to happen unless the black hole is extremely tiny, close by the Planck scale.

It is possible that the white hole which a black hole supposedly turns into is not the exact time-reverse, but instead another solution that further increases entropy. But in that case I don’t know where this solution comes from. And even so I would suspect that the kick required at the junction must be extremely finetuned. And either way, it’s not a problem I’ve seen addressed in the literature. (If anybody knows a reference, please let me know.)

The most likely thing to happen instead is that quantum fluctuations average out to give back the semi-classical limit. Hence, no white-hole transition. For the black-to-white-hole transition one would need quantum fluctuations to conspire together in just the right way. That’s possible. But it’s exceedingly unlikely.

In the other recent paper the authors find a surprisingly large transition rate for black to white holes. But they use a highly symmetrized configuration with very few degrees of freedom. This must vastly overestimate the probability for transition. It’s an interesting mathematical example, but it has very little to do with real black holes out there.

In summary: That black holes transition to white holes and in this way release information is an idea appealing because of its simplicity. But I remain unconvinced because I am missing a good argument demonstrating that such a process is likely to happen.

Tuesday, July 12, 2016

The first antenna of MeerKAT,
a SKA precursor in South Africa.
[Image Source.]

It’s hard to see black holes – after all, their defining feature is that they swallow light. But it’s also hard to discourage scientists from trying to shed light on mysteries. In a recent paper, a group of researchers from Long Island University and Virginia Tech have proposed a new way to probe the near-horizon region of black holes and, potentially, quantum gravitational effects.

The idea is simple and yet promising: Search for a binary system in which a pulsar and a black hole orbit around each other, then analyze the pulsar signal for unusual fluctuations.

A pulsar is a rapidly rotating neutron star that emits a focused beam of electromagnetic radiation. This beam goes into the direction of the poles of the magnetic field, and is normally not aligned with the neutron star’s axis of rotation. The beam therefore spins with a regular period like a lighthouse beacon. If Earth is located within the beam’s reach, our telescopes receive a pulse every time the beam points into our direction.

Pulsar timing can be extremely precise. We know some pulsars that have been flashing for decades every couple of milliseconds to a precision of a few microseconds. This high regularity allows astrophysicists to search for signals which might affect the timing. Fluctuations of space-time itself, for example, would increase the pulsar-timing uncertainty, a method that has been used to derive constraints on the stochastic gravitational wave background. And if a pulsar is in a binary system with a black hole, the pulsar’s signal might scrape by the black hole and thus encode information about the horizon which we can catch on Earth.

No such pulsar-black hole binaries are known to date. But upcoming experiments like eLISA and the Square Kilometer Array (SKA) will almost certainly detect new pulsars. In their paper, the authors estimate that SKA might observe up to 100 new pulsar-black hole binaries, and they put the probability that a newly discovered system would have a suitable orientation at roughly one in a hundred. If they are right, the SKA would have a good chance to find a promising binary.

Much of the paper is dedicated to arguing that the timing accuracy of such a binary pulsar could carry information about quantum gravitational effects. This is not impossible but speculative. Quantum gravitational effects are normally expect to be strong towards the black hole singularity, ie well inside the black hole and hidden from observation. Naïve dimensional estimates reveal that quantum gravity should be unobservably small in the horizon area.

However, this argument has recently been questioned in the aftermath of the firewall controversy surrounding black holes, because one solution to the black hole firewall paradox is that quantum gravitational effects can stretch over much longer distances than the dimensional estimates lead one to expect. Steve Giddings has long been a proponent of such long-distance fluctuations, and scenarios like black hole fuzzballs, or Dvali’s Bose-Einstein Computers also lead to horizon-scale deviations from general relativity. It is hence something that one should definitely look for.

Previous proposals to test the near-horizon geometry were based on measurements of gravitational waves from merger events or the black hole shadow, each of which could reveal deviations from general relativity. However, so far these were quite general ideas lacking quantitative estimates. To my knowledge, this paper is the first to demonstrate that it’s technologically feasible.

Michael Kavic, one of the authors of this paper, will attend our September conference on “Experimental Search for Quantum Gravity.” We’re still planning to life-streaming the talks, so stay tuned and you’ll get a chance to listen in.

Monday, July 04, 2016

Before the LHC turned on, theoretical physicists had high hopes the collisions would reveal new physics besides the Higgs. The chances of that happening get smaller by the day. The possibility still exists, but the absence of new physics so far has already taught us an important lesson: Nature isn’t natural. At least not according to theoretical physicists.

The reason that many in the community expected new physics at the LHC was the criterion of naturalness. Naturalness, in general, is the requirement that a theory should not contain dimensionless numbers that are either very large or very small. If that is so, then theorists will complain the numbers are “finetuned” and regard the theory as contrived and hand-made, not to say ugly.

Technical naturalness (originally proposed by ‘t Hooft) is a formalized version of naturalness which is applied in the context of effective field theories in particular. Since you can convert any number much larger than one into a number much smaller than one by taking its inverse, it’s sufficient to consider small numbers in the following. A theory is technically natural if all suspiciously small numbers are protected by a symmetry. The standard model is technically natural, except for the mass of the Higgs.

The Higgs is the only (fundamental) scalar we know and, unlike all the other particles, its mass receives quantum corrections of the order of the cutoff of the theory. The cutoff is assumed to be close by the Planck energy – that means the estimated mass is 15 orders of magnitude larger than the observed mass. This too-large mass of the Higgs could be remedied simply by subtracting a similarly large term. This term however would have to be delicately chosen so that it almost, but not exactly, cancels the huge Planck-scale contribution. It would hence require finetuning.

In the framework of effective field theories, a theory that is not natural is one that requires a lot of finetuning at high energies to get the theory at low energies to work out correctly. The degree of finetuning can, and has been, quantified in various measures of naturalness. Finetuning is thought of as unacceptable because the theory at high energy is presumed to be more fundamental. The physics we find at low energies, so the argument, should not be highly sensitive to the choice we make for that more fundamental theory.

Until a few years ago, most high energy particle theorists therefore would have told you that the apparent need to finetuning the Higgs mass means that new physics must appear nearby the energy scale where the Higgs will be produced. The new physics, for example supersymmetry, would avoid the finetuning.

There’s a standard tale they have about the use of naturalness arguments, which goes somewhat like this:

1) The electron mass isn’t natural in classical electrodynamics, and if one wants to avoid finetuning this means new physics has to appear at around 70 MeV. Indeed, new physics appears even earlier in form of the positron, rendering the electron mass technically natural.

2) The difference between the masses of the neutral and charged pion is not natural because it’s suspiciously small. To prevent fine-tuning one estimates new physics must appear around 700 MeV, and indeed it shows up in form of the rho meson.

3) The lack of flavor changing neutral currents in the standard model means that a parameter which could a priori have been anything must be very small. To avoid fine-tuning, the existence of the charm quark is required. And indeed, the charm quark shows up in the estimated energy range.

From these three examples only the last one was an actual prediction (Glashow, Iliopoulos, and Maiani, 1970). To my knowledge this is the only prediction that technical naturalness has ever given rise to – the other two examples are post-dictions.

Not exactly a great score card.

But well, given that the standard model – in hindsight – obeys this principle, it seems reasonable enough to extrapolate it to the Higgs mass. Or does it? Seeing that the cosmological constant, the only other known example where the Planck mass comes in, isn’t natural either, I am not very convinced.

A much larger problem with naturalness is that it’s a circular argument and thus a merely aesthetic criterion. Or, if you prefer, a philosophic criterion. You cannot make a statement about the likeliness of an occurrence without a probability distribution. And that distribution already necessitates a choice.

In the currently used naturalness arguments, the probability distribution is assumed to be uniform (or at least approximately uniform) in a range that can be normalized to one by dividing through suitable powers of the cutoff. Any other type of distribution, say, one that is sharply peaked around small values, would require the introduction of such a small value in the distribution already. But such a small value justifies itself by the probability distribution just like a number close to one justifies itself by its probability distribution.

Naturalness, hence, becomes a chicken-and-egg problem: Put in the number one, get out the number one. Put in 0.00004, get out 0.00004. The only way to break that circle is to just postulate that some number is somehow better than all other numbers.

The number one is indeed a special number in that it’s the unit element of the multiplication group. One can try to exploit this to come up with a mechanism that prefers a uniform distribution with an approximate width of one by introducing a probability distribution on the space of probability distributions, leading to a recursion relation. But that just leaves one to explain why that mechanism.

Another way to see that this can’t solve the problem is that any such mechanism will depend on the basis in the space of functions. Eg, you could try to single out a probability distribution by asking that it’s the same as its Fourier-transformation. But the Fourier-transformation is just one of infinitely many basis transformations in the space of functions. So again, why exactly this one?

Or you could try to introduce a probability distribution on the space of transformations among bases of probability distributions, and so on. Indeed I’ve played around with this for some while. But in the end you are always left with an ambiguity, either you have to choose the distribution, or the basis, or the transformation. It’s just pushing around the bump under the carpet.

The basic reason there’s no solution to this conundrum is that you’d need another theory for the probability distribution, and that theory per assumption isn’t part of the theory for which you want the distribution. (It’s similar to the issue with the meta-law for time-varying fundamental constants, in case you’re familiar with this argument.)

In any case, whether you buy my conclusion or not, it should give you a pause that high energy theorists don’t ever address the question where the probability distribution comes from. Suppose there indeed was a UV-complete theory of everything that predicted all the parameters in the standard model. Why then would you expect the parameters to be stochastically distributed to begin with?

This lacking probability distribution, however, isn’t my main issue with naturalness. Let’s just postulate that the distribution is uniform and admit it’s an aesthetic criterion, alrighty then. My main issue with naturalness is that it’s a fundamentally nonsensical criterion.

Any theory that we can conceive of which describes nature correctly must necessarily contain hand-picked assumptions which we have chosen “just” to fit observations. If that wasn’t so, all we’d have left to pick assumptions would be mathematical consistency, and we’d end up in Tegmark’s mathematical universe. In the mathematical universe then, we’d no longer have to choose a consistent theory, ok. But we’d instead have to figure out where we are, and that’s the same question in green.

All our theories contain lots of assumptions like Hilbert-spaces and Lie-algebras and Haussdorf measures and so on. For none of these is there any explanation other than “it works.” In the space of all possible mathematics, the selection of this particular math is infinitely fine-tuned already – and it has to be, for otherwise we’d be lost again in Tegmark space.

The mere idea that we can justify the choice of assumptions for our theories in any other way than requiring them to reproduce observations is logical mush. The existing naturalness arguments single out a particular type of assumption – parameters that take on numerical values – but what’s worse about this hand-selected assumption than any other hand-selected assumption?

This is not to say that naturalness is always a useless criterion. It can be applied in cases where one knows the probability distribution, for example for the typical distances between stars or the typical quantum fluctuation in the early universe, etc. I also suspect that it is possible to find an argument for the naturalness of the standard model that does not necessitate to postulate a probability distribution, but I am not aware of one.

It’s somewhat of a mystery to me why naturalness has become so popular in theoretical high energy physics. I’m happy to see it go out of the window now. Keep your eyes open in the next couple of years and you’ll witness that turning point in the history of science when theoretical physicists stopped dictating nature what’s supposedly natural.